Research Projects

DFG Project DI2160/3-1 (2020-2022) Robust estimation of time-varying moments, mutual information, and transfer entropy by means of quantile regression based density forecasts

Our goal is to simplify and accelerate the detection of non-linear structures and their characteristics in multivariate time series and cross-sectional data. To do so, we will examine the estimation of conditional and unconditional moments based on quantile regression. Therefore, we build on the ideas in Baur and Dimpfl (Journal of Financial Econometrics), to estimate the conditional variance of returns. Furthermore, we want to develop estimation and testing methods for relative entropy measures, such as mutual information or transfer entropy. The key to our proposed methodology is the decomposition of multivariate, joint density functions into conditional and unconditional densities which are needed to calculate entropy measures and moments. These can be modeled by a quantile regression. Due to its semi-parametric character and based on the available literature on the asymptotic theory of estimated quantiles, few assumptions are needed to model the densities, the computational effort is reduced, a smaller data size (compared to for example multivariate kernel density estimators) is sufficient and a consistent interpretation of the individual measures is to be expected. In particular, with the proposed method to calculate the entropy measures for continuous random variables, it is possible to dispense with the discretization of data which currently prevails in the literature. In addition, an asymptotic distribution theory for the entropy and moment estimators can be obtained by appropriate formulation of the quantile regression. This is the basis for developing for the first time flexible test procedures in the entropy context (as opposed to purely permutation-based tests), but also for novel tests for (conditional) moments of a random variable. Still, there are also new issues that need to be solved, like smoothing the estimated density functions, or the optimal support during the numerical integration. To investigate the advantages and disadvantages of the proposed methodology, in detail, is the focus of this project.